This paper presents numerical solutions of the slamming problem for 2-D wedges of small deadrise angles entering calm water. The compressibility of air between the bottom of the wedge and the free surface is modeled. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for water entry of wedges with various deadrise angles ranging from 0 to 10 degrees at constant vertical velocity. Computed pressures and air flows were compared with experimental data and the numerical solutions by other methods.


When a ship travels in heavy seas, the large-amplitude ship motion can result in bow-flare water impact. It will subsequently cause severe damages to ship structures. The water-entry problem of wedge has been extensively studies by many researchers. The theoretical analysis of the similarity flow induced by the wedge entry was first conducted Wagner (1932). Armand and Cointe (1986), Cointe (1991) and Howison et al. (1991) extended Wagner's theory to analyze the wedge entry problem using matched asymptotic expansions for wedges with small deadrise. Furthermore, Dobrovol'skaya (1969) developed an analytical solutions in terms of a nonlinear singular integral equation for the problem of the symmetrical entry of a wedge into calm water. Based on the work of Vinje and Brevig (1981), Greenhow (1987) used Cauchy's formula to solve the wedge entry problem.

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